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If \((2x)^3 = \sqrt{128}\) and \(x =\sqrt[n]{2}\) , what is the value of \(n\)?

 Jan 8, 2023
 #1
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The value of n is 8.

 Jan 8, 2023
 #2
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8x^3 = sqrt(128) = 8sqrt(2)

x^3 = sqrt(2) = (2)^0.5

So x = (2)^(1/2)(1/3). Thus, n = 6.

 Jan 8, 2023
edited by proyaop  Jan 8, 2023

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